Integrated Mini Case: HEDGING INTEREST RATE RISK WITH FUTURES CONTRACTS Use the following December 31, 2021 market value balance sheet for Bank One to answer the questions below. Assets (in thousands of $s) Liabilities/Equity (in thousands of $s) Value Duration Value Duration T-bills $1,500 0.75 NOW accounts $ 6,250 0.50 T-bonds 4,250 9.50 CDs 7,500 7.55 Loans 15,500 12.50 Federal funds 5,500 0.10 Equity 2,000 The bank’s manager thinks rates will increase by 0.50 percent in the next 3 months. To hedge this interest rate risk the manager will use June T-bond futures contracts. The T-bonds underlying the futures contracts have a maturity = 15 years, a duration = 14.25 years, and a price = 108-10 or $108,312.50. Assume that interest rate changes in the futures market relative to the cash market are such that br = 0.885. Calculate the leverage adjusted duration gap (DGAP) for Bank One. DA = [(T-bills/Total Value of Assets) (Duration of T- bills) + the same process for T-bonds + the same process for Loans = Expressed in years DL = [(NOW Accounts/Total Value of Liabilities)(Duration of NOW Accounts) + the same process for CDs + the same process for Federal funds] = Expressed in years Then you need to calculate the DGAP. DGAP=DA- (Total Liabilities/Total Assets)(DL) Using the DGAP model, if interest rates on assets and liabilities increase such that DRA/(1 + RA) = DRL/(1 +RL) = 0.0075, calculate the change in the value of assets and liabilities and the new value of the assets and liabilities for Bank One. ∆A = DA- x Total Assets x 0.0075 = -$1,764,375 => New asset value = Total Assets- ∆A = expressed in $ ∆L = DL x Total Liabilities x 0.0075 = expressed in $ Calculate the change in the market value of equity for Bank One if rates increase such that DR/(1 +R) = 0.0075. ∆E = DL x Total Assets x 0.0075 = $ Expressed in Dollars => New equity value = Equity Value from Balance Sheet in Problem in millions - ∆E = $ expressed in dollars Calculate the correct number of futures contracts needed to hedge the bank’s interest rate risk (do not round to the nearest whole contract). Make sure you specify whether you should enter the hedge with a short or long futures position. Nf== futures contracts Calculate the change in the bank’s market value of equity and the change in the value of the T-bond futures position for the bank if interest rates increase by 0.55 percent from the current rate of 6 percent on the T-bonds and increase 0.65 percent from the current rate of 8 percent on the balance sheet assets and liabilities. ∆E = DL x Total Assets x (0.0065/1.08) = ∆F = -14.25 x Amount of Futures Contract x 108,312.50 x (0.0055/1.06) = $1,025,717

Question

Integrated Mini Case: HEDGING INTEREST RATE RISK WITH FUTURES CONTRACTS

Use the following December 31, 2021 market value balance sheet for Bank One to answer the questions below.

Assets (in thousands of $s) Liabilities/Equity (in thousands of $s)

Value Duration Value Duration

T-bills $1,500 0.75 NOW accounts $ 6,250 0.50

T-bonds 4,250 9.50 CDs 7,500 7.55

Loans 15,500 12.50 Federal funds 5,500 0.10

Equity 2,000

The bank’s manager thinks rates will increase by 0.50 percent in the next 3 months. To hedge this interest rate risk the manager will use June T-bond futures contracts. The T-bonds underlying the futures contracts have a maturity = 15 years, a duration = 14.25 years, and a price = 108-10 or $108,312.50. Assume that interest rate changes in the futures market relative to the cash market are such that br = 0.885.

Calculate the leverage adjusted duration gap (DGAP) for Bank One.

D_A = [(T-bills/Total Value of Assets) (Duration of T- bills) + the same process for T-bonds + the same process for Loans = Expressed in years

D_L = [(NOW Accounts/Total Value of Liabilities)(Duration of NOW Accounts) + the same process for CDs + the same process for Federal funds] = Expressed in years

Then you need to calculate the DGAP.

DGAP=D_A- (Total Liabilities/Total Assets)(D_L)

Using the DGAP model, if interest rates on assets and liabilities increase such that DR_A/(1 + R_A) = DR_L/(1 +R_L) = 0.0075, calculate the change in the value of assets and liabilities and the new value of the assets and liabilities for Bank One.

∆A = D_A- x Total Assets x 0.0075 = -$1,764,375

=> New asset value = Total Assets- ∆A = expressed in $

∆L = D_L x Total Liabilities x 0.0075 = expressed in $

Calculate the change in the market value of equity for Bank One if rates increase such that DR/(1 +R) = 0.0075.

∆E = D_L x Total Assets x 0.0075 = $ Expressed in Dollars

=> New equity value = Equity Value from Balance Sheet in Problem in millions - ∆E = $ expressed in dollars

Calculate the correct number of futures contracts needed to hedge the bank’s interest rate risk (do not round to the nearest whole contract). Make sure you specify whether you should enter the hedge with a short or long futures position.

N_f== futures contracts

Calculate the change in the bank’s market value of equity and the change in the value of the T-bond futures position for the bank if interest rates increase by 0.55 percent from the current rate of 6 percent on the T-bonds and increase 0.65 percent from the current rate of 8 percent on the balance sheet assets and liabilities.

∆E = D_L x Total Assets x (0.0065/1.08) =

∆F = -14.25 x Amount of Futures Contract x 108,312.50 x (0.0055/1.06) = $1,025,717